Wald Statistics in high-dimensional PCA

In this study, we consider PCA for Gaussian observations X1, …, Xn with covariance Σ = ∑iλiPi in the ’effective rank’ setting with model complexity governed by r(Σ) ≔ tr(Σ)∕∥Σ∥. We prove a Berry-Essen type bound for a Wald Statistic of the spectral projector $\hat P_r$. This can be used to construct non-asymptotic goodness of fit tests and confidence ellipsoids for spectral projectors Pr. Using higher order pertubation theory we are able to show that our Theorem remains valid even when $\mathbf{r}(\Sigma) \gg \sqrt{n}$.

CHARGE SYMMETRY BREAKING IN dd → 4He π0 WITH WASA-at-COSY

Charge symmetry breaking effects can be used as an experimental tool to study quark mass effects. Using recent high precision data from TRIUMF and IUCF an international theory collaboration is working on a consistent description within the framework of chiral pertubation theory. The WASA-at-COSY collaboration has started an experimental program extending the studies on the reaction dd → 4 He π0 towards higher excess energies in order to provide necessary information on the contribution of p-waves. First preliminary results on the total cross section at Q = 60 MeV are presented.

PIONIC HYDROGEN

The measurement of the pion–nucleon scattering lengths constitutes a high–precision test of the methods of Chiral Pertubation Theory (χPT), which is the low–energy approach of QCD. The πN s–wave scattering lengths and the pion–nucleon coupling constant are related to the strong–interaction shift ∊1s and width Γ1s of the s–states in the pionic hydrogen atom. ∊1s and Γ1s are determined from the measured energies and line widths of X–ray transitions to the 1s ground state when compared to the calculated electromagnetic values. A new experiment, set up at the Paul–Scherrer–Institut (PSI), has completed a first series of measurements.

Polaron Energy Spectrum in a Disk-Shaped Quantum Dot

The energy spectrum of a weak coupling polaron is considered in a disk-shaped quantum dot. An analytical expression for the polaron energy correction to the ground and the first excited state is calculated using a modified pertubation theory. Anticrossing of the polaron energy levels in the dependence on the quantum dot radius is obtained.